Instability criteria for a motion of a vortex subject to a non-linear friction force

Here we study the instability of the vortex motion caused by non-monotonous dependence of the friction force on the vortex velocity in the presence of a gyroforce. The analysis is done within the frameworks of 'minimal' model for the elastic string subject to friction force and gyroforce. We demonstrate that even a weak gyroforce renders the condition for onset of instability more strict than for a vortex not subject to gyroforce: either the friction force must exceed a threshold, or its non-monotonic velocity dependence must be a rather steep function